Just because the "purpose" of the cosmos is irreconcilable with the purpose that one being defines for themselves, doesn't mean that purpose is nonsensical.

I use the word nonsensical over the word irrational, because there are many things in the world which you would term irrational. One of them is the emergence of intelligence (yes, you can rationalize this as an evolutionary adaption, but the basis of everything is irrational, so who cares?). Irrational though it is, we are still, to some extent, rational minds trapped in this irrational world. To dispose of any presupposition as irrational, simply for the sake of logical consistency, is an irresponsible way to live.

It is neither rational nor irrational to live as a solipsist. It is simply an axiom on which you base the rest of your rationalizations. Choose your axioms wisely, and the world will unfold accordingly.